Mutual Information of Population Codes and Distance Measures in Probability Space

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is developed. We show that this rate is controlled by a distance function between the response probabilities induced by different stimuli. This function, which we term the {\it Confusion Distance} between two probabilities, is related to the Renyi $\alpha$-Information.Comment: 11 pages, 3 figures, accepted to PR

Single-Subject Research in Psychiatry:Facts and Fictions

Scientific evidence in the field of psychiatry is mainly derived from group-based ("nomothetic") studies that yield group-aggregated results, while often the need is to answer questions that apply to individuals. Particularly in the presence of great inter-individual differences and temporal complexities, information at the individual-person level may be valuable for personalized treatment decisions, individual predictions and diagnostics. The single-subject study design can be used to make inferences about individual persons. Yet, the single-subject study is not often used in the field of psychiatry. We believe that this is because of a lack of awareness of its value rather than a lack of usefulness or feasibility. In the present paper, we aimed to resolve some common misconceptions and beliefs about single-subject studies by discussing some commonly heard "facts and fictions." We also discuss some situations in which the single-subject study is more or less appropriate, and the potential of combining single-subject and group-based study designs into one study. While not intending to plea for single-subject studies at the expense of group-based studies, we hope to increase awareness of the value of single-subject research by informing the reader about several aspects of this design, resolving misunderstanding, and providing references for further reading

Predicting recurrence of depression using cardiac complexity in individuals tapering antidepressants

It is currently unknown whether the complexity and variability of cardiac dynamics predicts future depression and whether within-subject change herein precedes the recurrence of depression. We tested this in an innovative repeated single-subject study in individuals who had a history of depression and were tapering their antidepressants. In 50 individuals, electrocardiogram (ECG) derived Interbeat-interval (IBI) time-series data were collected for 5 min every morning and evening, for 4 months. Usable data were obtained from 14 participants who experienced a transition (i.e., a clinically significant increase in depressive symptoms) and 14 who did not. The mean, standard deviation, Higuchi dimension and multiscale entropy, calculated from IBIs, were examined for time trends. These quantifiers were also averaged over a baseline period and compared between the groups. No consistent trends were observed in any quantifier before increases in depressive symptoms within individuals. The entropy baseline levels significantly differed between the two groups (morning: P value < 0.001, Cohen’s d = −2.185; evening: P value < 0.001, Cohen’s d = −1.797) and predicted the recurrence of depressive symptoms, in the current sample. Moreover, higher mean IBIs and Higuchi dimensions were observed in individuals who experienced transitions. While we found little evidence to support the existence of within- individual warning signals in IBI time-series data preceding an upcoming depressive transition, our results indicate that individuals who taper antidepressants and showed lower entropy of cardiac dynamics exhibited a higher chance of recurrence of depression. Hence, entropy could be a potential digital phenotype for assessing the risk of recurrence of depression in the short term while tapering antidepressants

Risk Ahead: Actigraphy-Based Early-Warning Signals of Increases in Depressive Symptoms During Antidepressant Discontinuation

Antidepressant discontinuation increases the risk of experiencing depressive symptoms. In a repeated single-subject design, we tested whether transitions in depression were preceded by increases in actigraphy-based critical-slowing-down-based early-warning signals (EWSs; variance, kurtosis, autocorrelation), circadian-rhythm-based indicators, and decreases in mean activity levels. Four months of data from 16 individuals with a transition in depression and nine without a transition in depression were analyzed using a moving-window method. As expected, more participants with a transition showed at least one EWS (50% true positives; 22.2% false positives). Increases in circadian rhythm variables (25.0% true positives vs. 44.4% false positives) and decreases in activity levels (37.5% true positives vs. 44.4% false positives) were more common in participants without a transition. None of the tested risk indicators could confidently predict upcoming transitions in depression, but some evidence was found that critical-slowing-down-based EWSs were more common in participants with a transition

Affective reactivity to daily life stress:Relationship to positive psychotic and depressive symptoms in a general population sample

Introduction: Increased affective reactivity to daily life stress has been found in individuals with psychosis and depression, and in those at risk for these conditions. Because depressive and psychotic symptoms often co-occur, increased affective reactivity in these disorders may be explained by the presence of depressive symptoms, psychotic symptoms, or both. Therefore, we examined whether affective reactivity to daily stress is related to positive psychotic symptoms, independently of depressive symptoms, and vice versa. Methods: We used data from an intensive sampling study in the general population (n = 411), with three measurements a day (t = 90). The following subjective stressors were assessed: appraisal of activities, appraisal of social interactions, and experienced physical discomfort. Affective reactivity was conceptualized as both the positive affect (PA) and negative affect (NA) response to these stressors. By means of mixed model analyses, it was examined whether affective reactivity was independently related to depressive and/or positive psychotic symptoms. Results: The PA response to activities and NA response to social interactions were negatively and positively related to depressive symptoms, respectively, independent of psychotic symptoms. In contrast, no (in) dependent association was found between positive psychotic symptoms and affective reactivity to any of the daily life stressors. These findings were confirmed in a subsample with increased symptoms.  Limitations: The prevalence of positive psychotic symptoms was relatively low in this general population sample. Conclusions: Increased affect reactivity predicts depressive symptoms, but not positive psychotic symptoms. Affective reactivity may still facilitate the development of psychotic symptomatology via its impact on depressive symptoms

Chiral symmetry restoration and the Z3 sectors of QCD

Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.Comment: 4 pages, 4 figure

Yang-Mills Theory as a Deformation of Topological Field Theory, Dimensional Reduction and Quark Confinement

We propose a reformulation of Yang-Mills theory as a perturbative deformation of a novel topological (quantum) field theory. We prove that this reformulation of the four-dimensional QCD leads to quark confinement in the sense of area law of the Wilson loop. First, Yang-Mills theory with a non-Abelian gauge group G is reformulated as a deformation of a novel topological field theory. Next, a special class of topological field theories is defined by both BRST and anti-BRST exact action corresponding to the maximal Abelian gauge leaving the maximal torus group H of G invariant. Then we find the topological field theory ($D>2$) has a hidden supersymmetry for a choice of maximal Abelian gauge. As a result, the D-dimensional topological field theory is equivalent to the (D-2)-dimensional coset G/H non-linear sigma model in the sense of Parisi and Sourlas dimensional reduction. After maximal Abelian gauge fixing, the topological property of magnetic monopole and anti-monopole of four-dimensional Yang-Mills theory is translated into that of instanton and anti-instanton in two-dimensional equivalent model. It is shown that the linear static potential in four-dimensions follows from the instanton--anti-instanton gas in the equivalent two-dimensional non-linear sigma model obtained from the four-dimensional topological field theory by dimensional reduction, while the remaining Coulomb potential comes from the perturbative part in four-dimensional Yang-Mills theory. The dimensional reduction opens a path for applying various exact methods developed in two-dimensional quantum field theory to study the non-perturbative problem in low-energy physics of four-dimensional quantum field theories.Comment: 58 pages, Latex, no figures, version accepted for publication in Phys. Rev. D (additions of Discussion, references and minor changes

The Green River Natural Analogue as a field laboratory to study the long-term fate of CO2 in the subsurface

Understanding the long-term response of CO2 injected into porous reservoirs is one of the most important aspects to demonstrate safe and permanent storage. In order to provide quantitative constraints on the long-term impacts of CO2-charged fluids on the integrity of reservoir-caprock systems we recovered some 300m of core from a scientific drill hole through a natural CO2 reservoir, near Green River, Utah. We obtained geomechanical, mineralogical, geochemical, petrophysical and mineralogical laboratory data along the entire length of the core and from non CO2-charged control samples. Furthermore, we performed more detailed studies through portions of low permeability layers in direct contact with CO2-charged layers. This was done to constrain the nature and penetration depths of CO2-promoted fluid-mineral reaction fronts. The major reactions identified include the dissolution of diagenetic dolomite cements and hematite grain coatings, and the precipitation of ankerite and pyrite and have been used as input for geochemical 1D reactive transport modelling, to constrain the magnitude and velocity of the mineral-fluid reaction front. In addition, we compared geomechanical data from the CO2-exposed core and related unreacted control samples to assess the mechanical stability of reservoir and seal rocks in a CO2 storage complex following mineral dissolution and precipitation for thousands of years. The obtained mechanical parameters were coupled to mineralogy and porosity. Key aim of this work was to better quantify the effect of long-term chemical CO2/brine/rock interactions on the mechanical strength and elastic properties of the studied formations